Different types of solvability conditions
for differential operators

Sergey G. Kryzhevich, Vitaly A. Volpert
Abstract:
Solvability conditions for linear differential equations
are usually formulated in terms of orthogonality of the right-hand side
to solutions of the homogeneous adjoint equation.
However, if the corresponding operator does not satisfy the
Fredholm property such solvability conditions may be not applicable.
For this case, we obtain another type of solvability conditions,
for ordinary differential equations on the real axis,
and for elliptic problems in unbounded cylinders.